A weaker condition for transitivity in probabilistic support

Abstract

Probabilistic support is not transitive. There are cases in which x probabilistically supports y, i.e., Pr(y | x) > Pr(y), y, in turn, probabilistically supports z, and yet it is not the case that x probabilistically supports z. Tomoji Shogenji, though, establishes a condition for transitivity in probabilistic support, that is, a condition such that, for any x, y, and z, if Pr(y | x) > Pr(y), Pr(z | y) > Pr(z), and the condition in question is satisfied, then Pr(z | x) > Pr(z). I argue for a second and weaker condition for transitivity in probabilistic support. This condition, or the principle involving it, makes it easier (than does the condition Shogenji provides) to establish claims of probabilistic support, and has the potential to play an important role in at least some areas of philosophy.